Research On Vibration Characteristics Of Arbitrarily-shaped Triangular And Quadrilateral Plates

Irregular plate structures often appear in practical engineering applications due to the complexity of the overall structure,such as civil engineering,aerospace engineering,marine and offshore engineering.It has very important engineering application value to master the vibration features of irregular structure.However,so far,most of the research on the vibration characteristics of the plate structure has focused on the regular shape plate structure,and the boundary condition form is also relatively simple.The improved Fourier series method has attracted much attention because it does not need to divide grids and can simulate elastic boundaries with artificial springs.Based on the improved Fourier series method,this paper establishes a set of efficient methods for analyzing the vibration characteristics of arbitrarily-shaped straight-sided quadrilateral and triangular plate structures by introducing a set of four-node coordinate transformations suitable for triangles and quadrilaterals.Firstly,on the basis of the classical thin plate theory,the straight-sided triangular and quadrilateral plates of atbitrary shapes are uniformly transformed into unit squre plates,the displacement admissible function of the squre plate is constructed by the improved Fourier series method.The boundary conditions of the springs are simulated by two sets of in-plane displacement constrained springs.Then the in-plane vibration analysis model for the arbitrary straight-sided triangular and quadrilateral plate can be established according to the Rayleigh-Ritz energy method.Simultaneous calculation of bending vibration and in-plane vibration is carried out to establish a unified vibration analysis model for orthotropic arbitrary straight-sided triangular and quadrilateral thin plates.After verifying the convergence and correctness of the established model,the natural frequencies of orthotropic plate structures with different geometric parameters,material parameters and boundary conditions are calculated to analyze the effects of these parameters on their vibration characteristics.The free vibration characteristics of the arbitrary straight-sided triangular and quadrilateral plate were studied based on the simple first-order shear deformation palte theory.This theory contains only four unkown displacement components.The displacement admissible function of a plate with arbitrary shape is expressed by the superposition of Fourier cosine series and sine series,and all the unkown Fourier coefficients are determined by Rayleigh-Ritz energy method.The convergence and accuracy of the method are verified by comparing numerical and experimental examples of plates with different boundary conditions and geometric parameters.Based on the energy principle,the vibration analysis model of the arbitrary straight-sided triangular and quadrilateral plate with cutouts was established.The energy equation for the plate before the opening is calculated by the coordinate transformation,and the energy equation of the plate corresponding to the opening is calculated in the original coordinate system.The vibration natural frequency parameters of the apertured plate structure under different geometric parameters and boundary conditions are given,and the correctness of the method is verified by comparison with related literature and finite element results.